TY - JOUR

T1 - Onset of convection in a moderate aspect-ratio rotating cylinder

T2 - Eckhaus-Benjamin-Feir instability

AU - Lopez, Juan

AU - Marques, F.

AU - Mercader, I.

AU - Batiste, O.

N1 - Funding Information:
Stimulating discussions with R. E. Ecke are very much appreciated. This work was supported by the National Science Foundation grant DMS-0505489, the Spanish grants FIS2004-01336 and FIS2006-08954, and Catalan grant SGR-00024. Computational resources of ASU’s Fulton HPCI are greatly appreciated.

PY - 2007/11/11

Y1 - 2007/11/11

N2 - A numerical study of the onset of thermal convection in a rotating circular cylinder of radius-to-depth ratio equal to four is considered in a regime dominated by the Coriolis force where the onset is to so-called wall modes. The wall modes consist of hot and cold pairs of thermal plumes rising and descending in the cylinder wall boundary layer, forming an essentially one-dimensional pattern characterized by the number of hot/cold plume pairs, m. In the limit of zero centrifugal force, this onset of convection at a critical temperature difference across the depth of the cylinder is via a symmetry-breaking supercritical Hopf bifurcation which leads to retrograde precession of the pattern with respect to the rotation of the cylinder. For temperature differences greater than critical, a number of distinct wall modes, distinguished by m, coexist and are stable. Their dynamics are controlled by an Eckhaus-Benjamin-Feir instability, the most basic features of which had been captured by a complex Ginzburg-Landau equation model. Here, we analyse this instability in rotating convection using direct numerical simulations of the Navier-Stokes equations in the Boussinesq approximation. Several properties of the wall modes are computed, extending the results to far beyond the onset of convection. Extensive favourable comparisons between our numerical results and previous experimental observations and complex Ginzburg-Landau model results are made.

AB - A numerical study of the onset of thermal convection in a rotating circular cylinder of radius-to-depth ratio equal to four is considered in a regime dominated by the Coriolis force where the onset is to so-called wall modes. The wall modes consist of hot and cold pairs of thermal plumes rising and descending in the cylinder wall boundary layer, forming an essentially one-dimensional pattern characterized by the number of hot/cold plume pairs, m. In the limit of zero centrifugal force, this onset of convection at a critical temperature difference across the depth of the cylinder is via a symmetry-breaking supercritical Hopf bifurcation which leads to retrograde precession of the pattern with respect to the rotation of the cylinder. For temperature differences greater than critical, a number of distinct wall modes, distinguished by m, coexist and are stable. Their dynamics are controlled by an Eckhaus-Benjamin-Feir instability, the most basic features of which had been captured by a complex Ginzburg-Landau equation model. Here, we analyse this instability in rotating convection using direct numerical simulations of the Navier-Stokes equations in the Boussinesq approximation. Several properties of the wall modes are computed, extending the results to far beyond the onset of convection. Extensive favourable comparisons between our numerical results and previous experimental observations and complex Ginzburg-Landau model results are made.

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U2 - 10.1017/S0022112007008038

DO - 10.1017/S0022112007008038

M3 - Article

AN - SCOPUS:35948938900

VL - 590

SP - 187

EP - 208

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -